Bayesian Statistics Documents

Showing 1 to 11 of 11

Department of Statistics, University of Chicago
'
2014
$
An Overview of Objective Bayes Estimation
Jim Berger
Duke University and University of Chicago
Department of Statistics
University of Chicago, 2014
&
1
%
Department of Statistics, University of Chic

Bayesian Inference: Introduction
Preamble: Probability and Uncertainty
In Bayesian statistics, we use the calculus of probability to represent uncertainty.
Sometimes people (including possibly me!) will say that Bayesian statistics treats
things about whi

The Meaning of Probability
Acknowledgments
Some of these notes are based on ones provided to me by Peter Donnelly, which he used to
teach a similar class at the University of Chicago in the 1990s.
Selected Books
Berger, J.O. Statistical Decision Theory a

Simple Examples of Bayesian Statistics
The following examples are intended to give very simple illustrations of the use of Bayes
Theorem to compute posterior distributions from prior distributions. They also introduce
some important terminology:
The poste

Hierarchical Modeling and Exchangeability (see also Bernardo and Smith, Ch.
Note: these notes are work in progress, particularly the earlier material focussed on hierarchical modeling.
1
Hierarchical modelling
1.1
Examples:
In genomics there are many sett

3
Prior Distributions
There are several different approaches to specification of prior distributions. We can identify
at least three different types of specification:
1. Subjective specification: the prior is chosen by making a serious attempt to quantify

Multiple Testing
1
Multiple Testing
In practice, particularly in modern scientific applications, one is often faced with
the problem of testing not just one null hypothesis, but many.
Example 1: In brain imaging one might collect brain image data on two g

4
4.1
Posterior Distributions
Posterior Summaries
In a Bayesian analysis, the posterior distribution encapsulates beliefs which have been updated in
the light of the data. Various natural summaries of the posterior are available.
Point Estimates
Three nat